equations demonstrating that “this interval [will be] proportional to the square root of time.”24 This prediction has held up with stunning precision.
Stock prices in the United States over the past sixty-odd years have behaved almost exactly as Bachelier said they would. Two-thirds of the time, they have moved within a range of 59 percent on either side of their average level in the course of a month. But the range in the course of a year has not been 72 percent, or twelve times as much; rather, it has averaged around 20 percent, or about three and a half times the monthly range. The square root of 12 is 3.46!
If stock prices vary according to the square root of time, they bear a remarkable resemblance to molecules randomly colliding with one another as they move in space. An English physicist named Robert Brown discovered this phenomenon early in the nineteenth century, and it is generally known as Brownian motion. Brownian motion was a critical ingredient of Einstein’s theory of the atom. The mathematical formula that describes this phenomenon was one of Bachelier’s crowning achievements.
Over time, in the literature on finance, Brownian motion came to be called the random walk, which someone once described as the path a drunk might follow at night in the light of a lamppost. No one knows who first used this expression, but it became increasingly familiar among academics during the 1960s, much to the annoyance of financial practitioners. Eugene Fama of the University of Chicago, one of the first and most enthusiastic proponents of the concept, tells me that random walk “is an ancient statistical term; nobody alive can claim it.”25 In later years, the primary focus of research on capital markets was on determining whether or not the random walk is a valid description of security price movements.
Bachelier himself, hardly a modest man, ended his dissertation with this flat statement: “It is evident that the present theory resolves the majority of problems in the study of speculation by the calculus of probability.”26
Despite its importance, Bachelier’s thesis was lost until it was rediscovered quite by accident in the 1950s by Jimmie Savage, a mathematical statistician at Chicago. Savage himself is worth a story. Milton Friedman, after associating with Savage for twenty years, described him as “.. one of the few really creative people I have met in the course of my intellectual life… Here is one of those extraordinary people of whom there are only a handful in any university at any time.”27
Savage’s parents delayed in giving him a first name because his mother was seriously ill when he was born in 1917. They later named him Leonard, but a nurse in the hospital had called him Jimmie and entered that name in the hospital records. Many years later, Savage arranged for a court order to make it official: His name became Leonard Jimmie Savage.
A child prodigy, Savage was afflicted with poor eyesight – he once confessed that “my eyes are too weak for much mischief.”28 When attending a public lecture, he was wont to walk up to the platform, examining the equations on the blackboard with a high-powered glass that he carried for the purpose. He once described himself this way: “I am a man of very many words. If I were to speak extemporaneously, I could probably hold myself spellbound for an hour.”29
Perhaps he was right to be spellbound: In the course of an outstanding career in various applied and theoretical areas of mathematics, Savage was offered faculty appointments by major universities in departments of biology, economics, management, and physics, in addition to mathematics.
Some time around 1954, while rummaging through a university library, Savage chanced upon a small book by Bachelier, published in 1914, on speculation and investment. Fascinated, he sent postcards to his economist friends, asking “Ever heard of this guy?”30 Paul Samuelson, who was just then beginning to explore theories of market behavior and valuation on his own, could not find the book in the MIT library, but he did discover a copy of Bachelier’s Ph.D. thesis. Samuelson has remarked that “Bachelier seems to have had something of a one-track mind. But what a track!”31 He immediately recognized the quality of Bachelier’s work and spread the word throughout the economics profession. Bachelier’s influence is apparent in Samuelson’s early treatment of the behavior of speculative prices.
Even if Bachelier had been better known in his lifetime, few people would have paid much attention to what he had to say. Those who controlled the real world of finance in the United States had little interest in the inner workings of the stock market. Playing the market was just too much fun. Stock prices rose 60 percent from 1900 to 1916, declining in only four of those years. From 1921 to 1929, as the American industrial juggernaut linked itself to the nation’s farms through the rapidly expanding railroad system, stock prices soared sixfold.
By 1900, Thomas Edison’s stock tickers had been punching out prices for nearly thirty years. The streets of the financial district swarmed all day, and often into the night, with young boys rushing to deliver the latest news bulletins.
For many years those bulletins were inscribed by hand with a stylus on a sheaf of tissue and carbon paper that produced up to 24 copies at a time. Until the introduction of small, hand-cranked printing presses in the mid-1880s and then the Dow, Jones news ticker in 1897, these handwritten bulletins were the main source of information for Wall Street traders and investors. Dow, Jones & Co. continued to deliver bulletins by messenger up to the end of World War II.
Recipes for predicting stock prices were in urgent demand on Wall Street throughout these years. By far the most famous was the Dow Theory, developed by Charles Dow, co-founder of Dow, Jones & Co. in 1882 and the first editor of the company’s flagship publication. The Wall Street Journal, launched in 1889.
Dow was born in a small town in Connecticut in 1851. He had had twenty jobs before he found his real love in journalism when he went to work as a reporter and part-time printer at the Springfield (Massachusetts) Republican in 1869. The editor, Samuel Bowles, a brilliant though difficult man, was one of the first editors to insist that the lead paragraph of an article should tell the whole story in brief: “who, what, when, where, and why.”
In 1875, Dow left Springfield to join the Providence Journal, where he attracted national attention with a series of articles on the history of steam transportation. In those articles he concentrated on the efforts of the sailing freighters to withstand the inroads of the steamboat companies, many of which were forming joint ventures with the expanding railroad system.
In 1879, a group of eastern financiers, along with Senator Jerome Bonaparte Chaffee of Colorado, invited Dow to join them on a visit to Leadville, Colorado, the site of a huge silver strike. One of the mines, the Camp Bird mine, had been discovered by three Gallagher brothers – Irish laborers who on their arrival in Leadville had been refused credit for a few loaves of bread. The town had a population of 18,000 when Dow arrived; two years earlier, before the Gallaghers arrived on the scene, the mining camp had consisted of nothing but tents. There were numerous hotels and establishments when Dow arrived. And there were dancing houses where ladies charged 50 cents for a set of dances. In Dow’s words, those ladies had “descended to the very root of the soiled ladder.”32
After three months, the Easterners had had enough. Dow’s last article from Leadville to the Providence Journal quoted one member of the party, about to down a last glass of beer, who said, “Be it ever so humble, there’s no place like Fifth Avenue.”33
Dow returned home convinced that the economic future of America was almost unlimited. His experience
Bachelier (1900).
Fama, PC&I.
Bachelier (1900).
Wallis (1981).
Wallis (1981).
Wallis (1981).
Samuelson, PC&I.
Samuelson (1973).
Wendt (1982).
Wendt (1982).
